Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 88.8% → 99.8%

Time: 9.5s

Alternatives: 10

Speedup: 1.0×

• 48.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\sin x \cdot \sinh y}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (sin x) (sinh y)) x))

C

double code(double x, double y) {
	return (sin(x) * sinh(y)) / x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (sin(x) * sinh(y)) / x
end function

Java

public static double code(double x, double y) {
	return (Math.sin(x) * Math.sinh(y)) / x;
}

Python

def code(x, y):
	return (math.sin(x) * math.sinh(y)) / x

Julia

function code(x, y)
	return Float64(Float64(sin(x) * sinh(y)) / x)
end

MATLAB

function tmp = code(x, y)
	tmp = (sin(x) * sinh(y)) / x;
end

Wolfram

code[x_, y_] := N[(N[(N[Sin[x], $MachinePrecision] * N[Sinh[y], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]

Initial Program: 88.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\sin x \cdot \sinh y}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (sin x) (sinh y)) x))

C

double code(double x, double y) {
	return (sin(x) * sinh(y)) / x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (sin(x) * sinh(y)) / x
end function

Java

public static double code(double x, double y) {
	return (Math.sin(x) * Math.sinh(y)) / x;
}

Python

def code(x, y):
	return (math.sin(x) * math.sinh(y)) / x

Julia

function code(x, y)
	return Float64(Float64(sin(x) * sinh(y)) / x)
end

MATLAB

function tmp = code(x, y)
	tmp = (sin(x) * sinh(y)) / x;
end

Wolfram

code[x_, y_] := N[(N[(N[Sin[x], $MachinePrecision] * N[Sinh[y], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sin x \cdot \frac{\sinh y}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (sin x) (/ (sinh y) x)))

C

double code(double x, double y) {
	return sin(x) * (sinh(y) / x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = sin(x) * (sinh(y) / x)
end function

Java

public static double code(double x, double y) {
	return Math.sin(x) * (Math.sinh(y) / x);
}

Python

def code(x, y):
	return math.sin(x) * (math.sinh(y) / x)

Julia

function code(x, y)
	return Float64(sin(x) * Float64(sinh(y) / x))
end

MATLAB

function tmp = code(x, y)
	tmp = sin(x) * (sinh(y) / x);
end

Wolfram

code[x_, y_] := N[(N[Sin[x], $MachinePrecision] * N[(N[Sinh[y], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.6%

   \[\frac{\sin x \cdot \sinh y}{x} \]
2. Step-by-step derivation

   1. associate-*r/ 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

4. Final simplification 99.9%

   \[\leadsto \sin x \cdot \frac{\sinh y}{x} \]

Alternative 2: 87.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -420 \lor \neg \left(y \leq 860000\right):\\ \;\;\;\;\mathsf{log1p}\left(\mathsf{expm1}\left(y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{x}{\sin x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -420.0) (not (<= y 860000.0)))
   (log1p (expm1 y))
   (/ y (/ x (sin x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -420.0) || !(y <= 860000.0)) {
		tmp = log1p(expm1(y));
	} else {
		tmp = y / (x / sin(x));
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -420.0) || !(y <= 860000.0)) {
		tmp = Math.log1p(Math.expm1(y));
	} else {
		tmp = y / (x / Math.sin(x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -420.0) or not (y <= 860000.0):
		tmp = math.log1p(math.expm1(y))
	else:
		tmp = y / (x / math.sin(x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -420.0) || !(y <= 860000.0))
		tmp = log1p(expm1(y));
	else
		tmp = Float64(y / Float64(x / sin(x)));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -420.0], N[Not[LessEqual[y, 860000.0]], $MachinePrecision]], N[Log[1 + N[(Exp[y] - 1), $MachinePrecision]], $MachinePrecision], N[(y / N[(x / N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -420 or 8.6e5 < y

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 4.2%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]

   5. Taylor expanded in x around 0 16.4%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]
   6. Step-by-step derivation

      1. div-inv 16.4%

         \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot \frac{1}{x}} \]

      2. associate-*l* 3.9%

         \[\leadsto \color{blue}{y \cdot \left(x \cdot \frac{1}{x}\right)} \]

      3. div-inv 3.9%

         \[\leadsto y \cdot \color{blue}{\frac{x}{x}} \]

      4. *-inverses 3.9%

         \[\leadsto y \cdot \color{blue}{1} \]

      5. *-commutative 3.9%

         \[\leadsto \color{blue}{1 \cdot y} \]

      6. *-un-lft-identity 3.9%

         \[\leadsto \color{blue}{y} \]

      7. log1p-expm1-u 73.9%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(y\right)\right)} \]

   7. Applied egg-rr 73.9%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(y\right)\right)} \]

   if -420 < y < 8.6e5

   1. Initial program 78.8%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.8%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 77.9%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
   5. Step-by-step derivation

      1. associate-/l* 98.9%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

   6. Simplified 98.9%

      \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -420 \lor \neg \left(y \leq 860000\right):\\ \;\;\;\;\mathsf{log1p}\left(\mathsf{expm1}\left(y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{x}{\sin x}}\\ \end{array} \]

Alternative 3: 66.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+254}:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+162} \lor \neg \left(y \leq 2.25 \cdot 10^{+157}\right):\\ \;\;\;\;\sqrt{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.8e+254)
   (/ (* x y) x)
   (if (or (<= y -1.2e+162) (not (<= y 2.25e+157)))
     (sqrt (* y y))
     (* (sin x) (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.8e+254) {
		tmp = (x * y) / x;
	} else if ((y <= -1.2e+162) || !(y <= 2.25e+157)) {
		tmp = sqrt((y * y));
	} else {
		tmp = sin(x) * (y / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-5.8d+254)) then
        tmp = (x * y) / x
    else if ((y <= (-1.2d+162)) .or. (.not. (y <= 2.25d+157))) then
        tmp = sqrt((y * y))
    else
        tmp = sin(x) * (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5.8e+254) {
		tmp = (x * y) / x;
	} else if ((y <= -1.2e+162) || !(y <= 2.25e+157)) {
		tmp = Math.sqrt((y * y));
	} else {
		tmp = Math.sin(x) * (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.8e+254:
		tmp = (x * y) / x
	elif (y <= -1.2e+162) or not (y <= 2.25e+157):
		tmp = math.sqrt((y * y))
	else:
		tmp = math.sin(x) * (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.8e+254)
		tmp = Float64(Float64(x * y) / x);
	elseif ((y <= -1.2e+162) || !(y <= 2.25e+157))
		tmp = sqrt(Float64(y * y));
	else
		tmp = Float64(sin(x) * Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.8e+254)
		tmp = (x * y) / x;
	elseif ((y <= -1.2e+162) || ~((y <= 2.25e+157)))
		tmp = sqrt((y * y));
	else
		tmp = sin(x) * (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.8e+254], N[(N[(x * y), $MachinePrecision] / x), $MachinePrecision], If[Or[LessEqual[y, -1.2e+162], N[Not[LessEqual[y, 2.25e+157]], $MachinePrecision]], N[Sqrt[N[(y * y), $MachinePrecision]], $MachinePrecision], N[(N[Sin[x], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.7999999999999999e254

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 6.0%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]

   5. Taylor expanded in x around 0 78.0%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]

   if -5.7999999999999999e254 < y < -1.20000000000000005e162 or 2.24999999999999992e157 < y

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 5.2%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]

   5. Taylor expanded in x around 0 15.2%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]
   6. Step-by-step derivation

      1. div-inv 15.2%

         \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot \frac{1}{x}} \]

      2. associate-*l* 4.4%

         \[\leadsto \color{blue}{y \cdot \left(x \cdot \frac{1}{x}\right)} \]

      3. div-inv 4.4%

         \[\leadsto y \cdot \color{blue}{\frac{x}{x}} \]

      4. *-inverses 4.4%

         \[\leadsto y \cdot \color{blue}{1} \]

      5. *-commutative 4.4%

         \[\leadsto \color{blue}{1 \cdot y} \]

      6. *-un-lft-identity 4.4%

         \[\leadsto \color{blue}{y} \]

      7. add-sqr-sqrt 3.6%

         \[\leadsto \color{blue}{\sqrt{y} \cdot \sqrt{y}} \]

      8. sqrt-unprod 71.2%

         \[\leadsto \color{blue}{\sqrt{y \cdot y}} \]

   7. Applied egg-rr 71.2%

      \[\leadsto \color{blue}{\sqrt{y \cdot y}} \]

   if -1.20000000000000005e162 < y < 2.24999999999999992e157

   1. Initial program 87.7%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 46.7%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
   5. Step-by-step derivation

      1. associate-/l* 58.9%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

      2. associate-/r/ 64.7%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]

   6. Simplified 64.7%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+254}:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+162} \lor \neg \left(y \leq 2.25 \cdot 10^{+157}\right):\\ \;\;\;\;\sqrt{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \end{array} \]

Alternative 4: 54.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+255}:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+158} \lor \neg \left(y \leq 2.25 \cdot 10^{+157}\right):\\ \;\;\;\;\sqrt{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{x \cdot 0.16666666666666666 + \frac{1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -9.8e+255)
   (/ (* x y) x)
   (if (or (<= y -2.2e+158) (not (<= y 2.25e+157)))
     (sqrt (* y y))
     (/ (/ y x) (+ (* x 0.16666666666666666) (/ 1.0 x))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -9.8e+255) {
		tmp = (x * y) / x;
	} else if ((y <= -2.2e+158) || !(y <= 2.25e+157)) {
		tmp = sqrt((y * y));
	} else {
		tmp = (y / x) / ((x * 0.16666666666666666) + (1.0 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-9.8d+255)) then
        tmp = (x * y) / x
    else if ((y <= (-2.2d+158)) .or. (.not. (y <= 2.25d+157))) then
        tmp = sqrt((y * y))
    else
        tmp = (y / x) / ((x * 0.16666666666666666d0) + (1.0d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -9.8e+255) {
		tmp = (x * y) / x;
	} else if ((y <= -2.2e+158) || !(y <= 2.25e+157)) {
		tmp = Math.sqrt((y * y));
	} else {
		tmp = (y / x) / ((x * 0.16666666666666666) + (1.0 / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -9.8e+255:
		tmp = (x * y) / x
	elif (y <= -2.2e+158) or not (y <= 2.25e+157):
		tmp = math.sqrt((y * y))
	else:
		tmp = (y / x) / ((x * 0.16666666666666666) + (1.0 / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -9.8e+255)
		tmp = Float64(Float64(x * y) / x);
	elseif ((y <= -2.2e+158) || !(y <= 2.25e+157))
		tmp = sqrt(Float64(y * y));
	else
		tmp = Float64(Float64(y / x) / Float64(Float64(x * 0.16666666666666666) + Float64(1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -9.8e+255)
		tmp = (x * y) / x;
	elseif ((y <= -2.2e+158) || ~((y <= 2.25e+157)))
		tmp = sqrt((y * y));
	else
		tmp = (y / x) / ((x * 0.16666666666666666) + (1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -9.8e+255], N[(N[(x * y), $MachinePrecision] / x), $MachinePrecision], If[Or[LessEqual[y, -2.2e+158], N[Not[LessEqual[y, 2.25e+157]], $MachinePrecision]], N[Sqrt[N[(y * y), $MachinePrecision]], $MachinePrecision], N[(N[(y / x), $MachinePrecision] / N[(N[(x * 0.16666666666666666), $MachinePrecision] + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.79999999999999943e255

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 6.0%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]

   5. Taylor expanded in x around 0 78.0%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]

   if -9.79999999999999943e255 < y < -2.2000000000000001e158 or 2.24999999999999992e157 < y

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 5.2%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]

   5. Taylor expanded in x around 0 15.2%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]
   6. Step-by-step derivation

      1. div-inv 15.2%

         \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot \frac{1}{x}} \]

      2. associate-*l* 4.4%

         \[\leadsto \color{blue}{y \cdot \left(x \cdot \frac{1}{x}\right)} \]

      3. div-inv 4.4%

         \[\leadsto y \cdot \color{blue}{\frac{x}{x}} \]

      4. *-inverses 4.4%

         \[\leadsto y \cdot \color{blue}{1} \]

      5. *-commutative 4.4%

         \[\leadsto \color{blue}{1 \cdot y} \]

      6. *-un-lft-identity 4.4%

         \[\leadsto \color{blue}{y} \]

      7. add-sqr-sqrt 3.6%

         \[\leadsto \color{blue}{\sqrt{y} \cdot \sqrt{y}} \]

      8. sqrt-unprod 71.2%

         \[\leadsto \color{blue}{\sqrt{y \cdot y}} \]

   7. Applied egg-rr 71.2%

      \[\leadsto \color{blue}{\sqrt{y \cdot y}} \]

   if -2.2000000000000001e158 < y < 2.24999999999999992e157

   1. Initial program 87.7%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 46.7%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
   5. Step-by-step derivation

      1. associate-/l* 58.9%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

      2. associate-/r/ 64.7%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]

   6. Simplified 64.7%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]
   7. Step-by-step derivation

      1. associate-/r/ 58.9%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

      2. div-inv 58.8%

         \[\leadsto \frac{y}{\color{blue}{x \cdot \frac{1}{\sin x}}} \]

      3. associate-/r* 64.6%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{\frac{1}{\sin x}}} \]

   8. Applied egg-rr 64.6%

      \[\leadsto \color{blue}{\frac{\frac{y}{x}}{\frac{1}{\sin x}}} \]

   9. Taylor expanded in x around 0 49.4%

      \[\leadsto \frac{\frac{y}{x}}{\color{blue}{0.16666666666666666 \cdot x + \frac{1}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+255}:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+158} \lor \neg \left(y \leq 2.25 \cdot 10^{+157}\right):\\ \;\;\;\;\sqrt{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{x \cdot 0.16666666666666666 + \frac{1}{x}}\\ \end{array} \]

Alternative 5: 49.1% accurate, 15.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.45 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+187}:\\ \;\;\;\;y \cdot \left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+256}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 1.45e+59)
   (* x (/ y x))
   (if (<= x 7.8e+187)
     (* y (+ 1.0 (* -0.16666666666666666 (* x x))))
     (if (<= x 8.2e+256) (/ x (/ x y)) (/ (* x y) x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 1.45e+59) {
		tmp = x * (y / x);
	} else if (x <= 7.8e+187) {
		tmp = y * (1.0 + (-0.16666666666666666 * (x * x)));
	} else if (x <= 8.2e+256) {
		tmp = x / (x / y);
	} else {
		tmp = (x * y) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 1.45d+59) then
        tmp = x * (y / x)
    else if (x <= 7.8d+187) then
        tmp = y * (1.0d0 + ((-0.16666666666666666d0) * (x * x)))
    else if (x <= 8.2d+256) then
        tmp = x / (x / y)
    else
        tmp = (x * y) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 1.45e+59) {
		tmp = x * (y / x);
	} else if (x <= 7.8e+187) {
		tmp = y * (1.0 + (-0.16666666666666666 * (x * x)));
	} else if (x <= 8.2e+256) {
		tmp = x / (x / y);
	} else {
		tmp = (x * y) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 1.45e+59:
		tmp = x * (y / x)
	elif x <= 7.8e+187:
		tmp = y * (1.0 + (-0.16666666666666666 * (x * x)))
	elif x <= 8.2e+256:
		tmp = x / (x / y)
	else:
		tmp = (x * y) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 1.45e+59)
		tmp = Float64(x * Float64(y / x));
	elseif (x <= 7.8e+187)
		tmp = Float64(y * Float64(1.0 + Float64(-0.16666666666666666 * Float64(x * x))));
	elseif (x <= 8.2e+256)
		tmp = Float64(x / Float64(x / y));
	else
		tmp = Float64(Float64(x * y) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 1.45e+59)
		tmp = x * (y / x);
	elseif (x <= 7.8e+187)
		tmp = y * (1.0 + (-0.16666666666666666 * (x * x)));
	elseif (x <= 8.2e+256)
		tmp = x / (x / y);
	else
		tmp = (x * y) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 1.45e+59], N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e+187], N[(y * N[(1.0 + N[(-0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e+256], N[(x / N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < 1.44999999999999995e59

   1. Initial program 88.5%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 36.2%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]

   5. Taylor expanded in x around 0 24.7%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]
   6. Step-by-step derivation

      1. associate-/l* 31.1%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{x}}} \]

      2. associate-/r/ 52.1%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]

   7. Applied egg-rr 52.1%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]

   if 1.44999999999999995e59 < x < 7.79999999999999962e187

   1. Initial program 99.9%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 30.9%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
   5. Step-by-step derivation

      1. associate-/l* 30.9%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

   6. Simplified 30.9%

      \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]
   7. Step-by-step derivation

      1. clear-num 30.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{x}{\sin x}}{y}}} \]

      2. associate-/r/ 30.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{\sin x}} \cdot y} \]

      3. clear-num 30.9%

         \[\leadsto \color{blue}{\frac{\sin x}{x}} \cdot y \]

   8. Applied egg-rr 30.9%

      \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot y} \]

   9. Taylor expanded in x around 0 39.8%

      \[\leadsto \color{blue}{\left(1 + -0.16666666666666666 \cdot {x}^{2}\right)} \cdot y \]
   10. Step-by-step derivation

       1. unpow2 39.8%

          \[\leadsto \left(1 + -0.16666666666666666 \cdot \color{blue}{\left(x \cdot x\right)}\right) \cdot y \]

   11. Simplified 39.8%

       \[\leadsto \color{blue}{\left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right)} \cdot y \]

   if 7.79999999999999962e187 < x < 8.20000000000000011e256

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 72.0%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]

   5. Taylor expanded in x around 0 25.0%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]
   6. Step-by-step derivation

      1. associate-/l* 4.8%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{x}}} \]

      2. associate-/r/ 45.4%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]

   7. Applied egg-rr 45.4%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]
   8. Step-by-step derivation

      1. *-commutative 45.4%

         \[\leadsto \color{blue}{x \cdot \frac{y}{x}} \]

      2. clear-num 49.3%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{x}{y}}} \]

      3. un-div-inv 49.3%

         \[\leadsto \color{blue}{\frac{x}{\frac{x}{y}}} \]

   9. Applied egg-rr 49.3%

      \[\leadsto \color{blue}{\frac{x}{\frac{x}{y}}} \]

   if 8.20000000000000011e256 < x

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 20.2%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]

   5. Taylor expanded in x around 0 27.9%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.45 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+187}:\\ \;\;\;\;y \cdot \left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+256}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \end{array} \]

Alternative 6: 49.7% accurate, 15.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.45 \cdot 10^{+59}:\\ \;\;\;\;\frac{\frac{y}{x}}{x \cdot 0.16666666666666666 + \frac{1}{x}}\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+187}:\\ \;\;\;\;y \cdot \left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+256}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 1.45e+59)
   (/ (/ y x) (+ (* x 0.16666666666666666) (/ 1.0 x)))
   (if (<= x 7.8e+187)
     (* y (+ 1.0 (* -0.16666666666666666 (* x x))))
     (if (<= x 6.5e+256) (/ x (/ x y)) (/ (* x y) x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 1.45e+59) {
		tmp = (y / x) / ((x * 0.16666666666666666) + (1.0 / x));
	} else if (x <= 7.8e+187) {
		tmp = y * (1.0 + (-0.16666666666666666 * (x * x)));
	} else if (x <= 6.5e+256) {
		tmp = x / (x / y);
	} else {
		tmp = (x * y) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 1.45d+59) then
        tmp = (y / x) / ((x * 0.16666666666666666d0) + (1.0d0 / x))
    else if (x <= 7.8d+187) then
        tmp = y * (1.0d0 + ((-0.16666666666666666d0) * (x * x)))
    else if (x <= 6.5d+256) then
        tmp = x / (x / y)
    else
        tmp = (x * y) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 1.45e+59) {
		tmp = (y / x) / ((x * 0.16666666666666666) + (1.0 / x));
	} else if (x <= 7.8e+187) {
		tmp = y * (1.0 + (-0.16666666666666666 * (x * x)));
	} else if (x <= 6.5e+256) {
		tmp = x / (x / y);
	} else {
		tmp = (x * y) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 1.45e+59:
		tmp = (y / x) / ((x * 0.16666666666666666) + (1.0 / x))
	elif x <= 7.8e+187:
		tmp = y * (1.0 + (-0.16666666666666666 * (x * x)))
	elif x <= 6.5e+256:
		tmp = x / (x / y)
	else:
		tmp = (x * y) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 1.45e+59)
		tmp = Float64(Float64(y / x) / Float64(Float64(x * 0.16666666666666666) + Float64(1.0 / x)));
	elseif (x <= 7.8e+187)
		tmp = Float64(y * Float64(1.0 + Float64(-0.16666666666666666 * Float64(x * x))));
	elseif (x <= 6.5e+256)
		tmp = Float64(x / Float64(x / y));
	else
		tmp = Float64(Float64(x * y) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 1.45e+59)
		tmp = (y / x) / ((x * 0.16666666666666666) + (1.0 / x));
	elseif (x <= 7.8e+187)
		tmp = y * (1.0 + (-0.16666666666666666 * (x * x)));
	elseif (x <= 6.5e+256)
		tmp = x / (x / y);
	else
		tmp = (x * y) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 1.45e+59], N[(N[(y / x), $MachinePrecision] / N[(N[(x * 0.16666666666666666), $MachinePrecision] + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e+187], N[(y * N[(1.0 + N[(-0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e+256], N[(x / N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < 1.44999999999999995e59

   1. Initial program 88.5%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 36.2%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
   5. Step-by-step derivation

      1. associate-/l* 47.6%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

      2. associate-/r/ 63.6%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]

   6. Simplified 63.6%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]
   7. Step-by-step derivation

      1. associate-/r/ 47.6%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

      2. div-inv 47.5%

         \[\leadsto \frac{y}{\color{blue}{x \cdot \frac{1}{\sin x}}} \]

      3. associate-/r* 63.5%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{\frac{1}{\sin x}}} \]

   8. Applied egg-rr 63.5%

      \[\leadsto \color{blue}{\frac{\frac{y}{x}}{\frac{1}{\sin x}}} \]

   9. Taylor expanded in x around 0 53.1%

      \[\leadsto \frac{\frac{y}{x}}{\color{blue}{0.16666666666666666 \cdot x + \frac{1}{x}}} \]

   if 1.44999999999999995e59 < x < 7.79999999999999962e187

   1. Initial program 99.9%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 30.9%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
   5. Step-by-step derivation

      1. associate-/l* 30.9%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

   6. Simplified 30.9%

      \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]
   7. Step-by-step derivation

      1. clear-num 30.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{x}{\sin x}}{y}}} \]

      2. associate-/r/ 30.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{\sin x}} \cdot y} \]

      3. clear-num 30.9%

         \[\leadsto \color{blue}{\frac{\sin x}{x}} \cdot y \]

   8. Applied egg-rr 30.9%

      \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot y} \]

   9. Taylor expanded in x around 0 39.8%

      \[\leadsto \color{blue}{\left(1 + -0.16666666666666666 \cdot {x}^{2}\right)} \cdot y \]
   10. Step-by-step derivation

       1. unpow2 39.8%

          \[\leadsto \left(1 + -0.16666666666666666 \cdot \color{blue}{\left(x \cdot x\right)}\right) \cdot y \]

   11. Simplified 39.8%

       \[\leadsto \color{blue}{\left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right)} \cdot y \]

   if 7.79999999999999962e187 < x < 6.50000000000000053e256

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 72.0%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]

   5. Taylor expanded in x around 0 25.0%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]
   6. Step-by-step derivation

      1. associate-/l* 4.8%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{x}}} \]

      2. associate-/r/ 45.4%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]

   7. Applied egg-rr 45.4%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]
   8. Step-by-step derivation

      1. *-commutative 45.4%

         \[\leadsto \color{blue}{x \cdot \frac{y}{x}} \]

      2. clear-num 49.3%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{x}{y}}} \]

      3. un-div-inv 49.3%

         \[\leadsto \color{blue}{\frac{x}{\frac{x}{y}}} \]

   9. Applied egg-rr 49.3%

      \[\leadsto \color{blue}{\frac{x}{\frac{x}{y}}} \]

   if 6.50000000000000053e256 < x

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 20.2%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]

   5. Taylor expanded in x around 0 27.9%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.45 \cdot 10^{+59}:\\ \;\;\;\;\frac{\frac{y}{x}}{x \cdot 0.16666666666666666 + \frac{1}{x}}\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+187}:\\ \;\;\;\;y \cdot \left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+256}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \end{array} \]

Alternative 7: 49.1% accurate, 18.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.45 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+187}:\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+256}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 1.45e+59)
   (* x (/ y x))
   (if (<= x 7.8e+187)
     (* -0.16666666666666666 (* y (* x x)))
     (if (<= x 7e+256) (/ x (/ x y)) (/ (* x y) x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 1.45e+59) {
		tmp = x * (y / x);
	} else if (x <= 7.8e+187) {
		tmp = -0.16666666666666666 * (y * (x * x));
	} else if (x <= 7e+256) {
		tmp = x / (x / y);
	} else {
		tmp = (x * y) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 1.45d+59) then
        tmp = x * (y / x)
    else if (x <= 7.8d+187) then
        tmp = (-0.16666666666666666d0) * (y * (x * x))
    else if (x <= 7d+256) then
        tmp = x / (x / y)
    else
        tmp = (x * y) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 1.45e+59) {
		tmp = x * (y / x);
	} else if (x <= 7.8e+187) {
		tmp = -0.16666666666666666 * (y * (x * x));
	} else if (x <= 7e+256) {
		tmp = x / (x / y);
	} else {
		tmp = (x * y) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 1.45e+59:
		tmp = x * (y / x)
	elif x <= 7.8e+187:
		tmp = -0.16666666666666666 * (y * (x * x))
	elif x <= 7e+256:
		tmp = x / (x / y)
	else:
		tmp = (x * y) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 1.45e+59)
		tmp = Float64(x * Float64(y / x));
	elseif (x <= 7.8e+187)
		tmp = Float64(-0.16666666666666666 * Float64(y * Float64(x * x)));
	elseif (x <= 7e+256)
		tmp = Float64(x / Float64(x / y));
	else
		tmp = Float64(Float64(x * y) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 1.45e+59)
		tmp = x * (y / x);
	elseif (x <= 7.8e+187)
		tmp = -0.16666666666666666 * (y * (x * x));
	elseif (x <= 7e+256)
		tmp = x / (x / y);
	else
		tmp = (x * y) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 1.45e+59], N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e+187], N[(-0.16666666666666666 * N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e+256], N[(x / N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < 1.44999999999999995e59

   1. Initial program 88.5%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 36.2%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]

   5. Taylor expanded in x around 0 24.7%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]
   6. Step-by-step derivation

      1. associate-/l* 31.1%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{x}}} \]

      2. associate-/r/ 52.1%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]

   7. Applied egg-rr 52.1%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]

   if 1.44999999999999995e59 < x < 7.79999999999999962e187

   1. Initial program 99.9%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 30.9%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
   5. Step-by-step derivation

      1. associate-/l* 30.9%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

   6. Simplified 30.9%

      \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]
   7. Step-by-step derivation

      1. clear-num 30.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{x}{\sin x}}{y}}} \]

      2. associate-/r/ 30.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{x}{\sin x}} \cdot y} \]

      3. clear-num 30.9%

         \[\leadsto \color{blue}{\frac{\sin x}{x}} \cdot y \]

   8. Applied egg-rr 30.9%

      \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot y} \]

   9. Taylor expanded in x around 0 39.8%

      \[\leadsto \color{blue}{\left(1 + -0.16666666666666666 \cdot {x}^{2}\right)} \cdot y \]
   10. Step-by-step derivation

       1. unpow2 39.8%

          \[\leadsto \left(1 + -0.16666666666666666 \cdot \color{blue}{\left(x \cdot x\right)}\right) \cdot y \]

   11. Simplified 39.8%

       \[\leadsto \color{blue}{\left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right)} \cdot y \]

   12. Taylor expanded in x around inf 39.8%

       \[\leadsto \color{blue}{-0.16666666666666666 \cdot \left(y \cdot {x}^{2}\right)} \]
   13. Step-by-step derivation

       1. unpow2 39.8%

          \[\leadsto -0.16666666666666666 \cdot \left(y \cdot \color{blue}{\left(x \cdot x\right)}\right) \]

   14. Simplified 39.8%

       \[\leadsto \color{blue}{-0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)} \]

   if 7.79999999999999962e187 < x < 6.9999999999999995e256

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 72.0%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]

   5. Taylor expanded in x around 0 25.0%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]
   6. Step-by-step derivation

      1. associate-/l* 4.8%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{x}}} \]

      2. associate-/r/ 45.4%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]

   7. Applied egg-rr 45.4%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]
   8. Step-by-step derivation

      1. *-commutative 45.4%

         \[\leadsto \color{blue}{x \cdot \frac{y}{x}} \]

      2. clear-num 49.3%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{x}{y}}} \]

      3. un-div-inv 49.3%

         \[\leadsto \color{blue}{\frac{x}{\frac{x}{y}}} \]

   9. Applied egg-rr 49.3%

      \[\leadsto \color{blue}{\frac{x}{\frac{x}{y}}} \]

   if 6.9999999999999995e256 < x

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 20.2%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]

   5. Taylor expanded in x around 0 27.9%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.45 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+187}:\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+256}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \end{array} \]

Alternative 8: 49.0% accurate, 29.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6.5 \cdot 10^{+256}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 6.5e+256) (* x (/ y x)) (/ (* x y) x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 6.5e+256) {
		tmp = x * (y / x);
	} else {
		tmp = (x * y) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 6.5d+256) then
        tmp = x * (y / x)
    else
        tmp = (x * y) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 6.5e+256) {
		tmp = x * (y / x);
	} else {
		tmp = (x * y) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 6.5e+256:
		tmp = x * (y / x)
	else:
		tmp = (x * y) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 6.5e+256)
		tmp = Float64(x * Float64(y / x));
	else
		tmp = Float64(Float64(x * y) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 6.5e+256)
		tmp = x * (y / x);
	else
		tmp = (x * y) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 6.5e+256], N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.50000000000000053e256

   1. Initial program 90.2%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 37.8%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]

   5. Taylor expanded in x around 0 23.6%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]
   6. Step-by-step derivation

      1. associate-/l* 27.2%

         \[\leadsto \color{blue}{\frac{y}{\frac{x}{x}}} \]

      2. associate-/r/ 47.8%

         \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]

   7. Applied egg-rr 47.8%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]

   if 6.50000000000000053e256 < x

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

         \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

   4. Taylor expanded in y around 0 20.2%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]

   5. Taylor expanded in x around 0 27.9%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6.5 \cdot 10^{+256}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \end{array} \]

Alternative 9: 50.0% accurate, 41.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{y}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x (/ y x)))

C

double code(double x, double y) {
	return x * (y / x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (y / x)
end function

Java

public static double code(double x, double y) {
	return x * (y / x);
}

Python

def code(x, y):
	return x * (y / x)

Julia

function code(x, y)
	return Float64(x * Float64(y / x))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (y / x);
end

Wolfram

code[x_, y_] := N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.6%

   \[\frac{\sin x \cdot \sinh y}{x} \]
2. Step-by-step derivation

   1. associate-*r/ 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

4. Taylor expanded in y around 0 37.0%

   \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]

5. Taylor expanded in x around 0 23.8%

   \[\leadsto \frac{\color{blue}{y \cdot x}}{x} \]
6. Step-by-step derivation

   1. associate-/l* 26.2%

      \[\leadsto \color{blue}{\frac{y}{\frac{x}{x}}} \]

   2. associate-/r/ 46.3%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]

7. Applied egg-rr 46.3%

   \[\leadsto \color{blue}{\frac{y}{x} \cdot x} \]

8. Final simplification 46.3%

   \[\leadsto x \cdot \frac{y}{x} \]

Alternative 10: 28.2% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 y)

C

double code(double x, double y) {
	return y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y
end function

Java

public static double code(double x, double y) {
	return y;
}

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

function tmp = code(x, y)
	tmp = y;
end

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 90.6%

   \[\frac{\sin x \cdot \sinh y}{x} \]
2. Step-by-step derivation

   1. associate-*r/ 99.9%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]

4. Taylor expanded in y around 0 37.0%

   \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
5. Step-by-step derivation

   1. associate-/l* 46.4%

      \[\leadsto \color{blue}{\frac{y}{\frac{x}{\sin x}}} \]

   2. associate-/r/ 59.5%

      \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]

6. Simplified 59.5%

   \[\leadsto \color{blue}{\frac{y}{x} \cdot \sin x} \]

7. Taylor expanded in x around 0 26.2%

   \[\leadsto \color{blue}{y} \]

8. Final simplification 26.2%

   \[\leadsto y \]

Developer target: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sin x \cdot \frac{\sinh y}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (sin x) (/ (sinh y) x)))

C

double code(double x, double y) {
	return sin(x) * (sinh(y) / x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = sin(x) * (sinh(y) / x)
end function

Java

public static double code(double x, double y) {
	return Math.sin(x) * (Math.sinh(y) / x);
}

Python

def code(x, y):
	return math.sin(x) * (math.sinh(y) / x)

Julia

function code(x, y)
	return Float64(sin(x) * Float64(sinh(y) / x))
end

MATLAB

function tmp = code(x, y)
	tmp = sin(x) * (sinh(y) / x);
end

Wolfram

code[x_, y_] := N[(N[Sin[x], $MachinePrecision] * N[(N[Sinh[y], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023257 
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (* (sin x) (/ (sinh y) x))

  (/ (* (sin x) (sinh y)) x))